In this paper, we develop, analyze and test the Fourier spectral methods for solving the Degasperis–Procesi (DP) equation which contains nonlinear high order derivatives, and possibly discontinuous or sharp transition solutions. The L2 stability is obtained for general numerical solutions of the Fourier Galerkin method and Fourier collocation (pseudospectral) method. By applying the Gegenbauer ...

For a number field K with ring of integers O K , we prove an analogue over finite rings of the form O K /P m of the Fundamental Theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where P is a big enough prime ideal of O K and m > 1. In the appendix, F. to the functional equation of L-functions of Dirichlet type associated with prehomogeneous vector spaces.

Methods are developed for extracting from a numerical propagating-beam solution of a scalar wave equation the information necessary to compute the impulse-response function and the pulse dispersion for a multimode graded-index fiber. It is shown that the scalar Helmholtz equation and the parabolic wave equation have the same set of eigenfunctions in common and that the eigenvalues for the two e...

We studied physical problems related to heat transport and the corresponding differential equations, which describe a wider range of physical processes. The operational method was employed to construct particular solutions for them. Inverse differential operators and operational exponent as well as operational definitions and operational rules for generalized orthogonal polynomials were used to...

in this article, a transversely isotropic linear elastic half-space with depth wise isotropy axis of material containing a cylindrical cavity of finite length is considered to be under the effect of an arbitrary torsion force applied on the wall of the cavity. to this end, the equation of equilibrium has been written in a cylindrical coordinate system, by dividing the involved domain to two reg...

Abstract An approach to find the field equation solution of the Randall-Sundrum model with the S/Z2 extra axis is presented. We closely examine the infrared singularity. The vacuum is set by the 5 dimensional Higgs field. Both the domain-wall and the anti-domain-wall naturally appear, at the ends of the extra compact axis, by taking a new infrared regularization. The stability is guaranteed fro...

We present a local Fourier analysis of multigrid methods for the two-dimensional curl-curl formulation of Maxwell's equations. Both the hybrid smoother proposed by Hiptmair and the overlapping block smoother proposed by Arnold, Falk and Winther are considered. The key to our approach is the identification of two-dimensional eigenspaces of the discrete curl-curl problem by decou-pling the Fourie...

We have studied the problem of diffraction of plane waves by a finite slit in an infinitely long soft-hard plane. Analysis is based on the Fourier transform, the Wiener-Hopf technique and the method of steepest descent. The boundary value problem is reduced to a matrix Wiener-Hopf equation which is solved by using the factorization of the kernel matrix. The diffracted field, calculated in the f...